电机学（第七版）（修订版）课件 Chapter-2-Transformers

Chapter2Transformers7/10/2024Transformers12.1IntroductionThetransformerconsistsoftwoormorecoils(orwindings)coupledbymutualmagneticfluxIftheprimarywindingisconnectedtoanalternatingvoltagesource,analternatingfluxwilllinkthesecondarywinding,inducinganalternatingsecondaryvoltageMosttransformersconsideredherehavehigh-permeabilityironcorestoincreasethedegreeofcouplingbetweenthewindings7/10/2024Transformers22.2No-loadconditionsWithsecondaryopen,thereisnoloadonthetransformerAlloftheprimarycurrentisexcitingcurrent,thatis,itgoestomagnetizethecoreandtoovercomecorelossesCurrentsandvoltagesareequivalentsinusoidalvalues7/10/2024Transformers3TransformerwithopensecondaryNo-loadphasordiagramNo-loadexcitationcurrentIe=Im+IcMagnetizingcurrentImlagsvoltageE1by90

Core-losscurrentIcisinphasewithvoltageE17/10/2024Transformers4No-loadphasordiagram2.3Effectofsecondarycurrent:idealtransformerIdealtransformermodel:Neglectlossesandmagnetizingcurrent,andassumeallthefluxinthemagneticcorelinksbothwindingsFaraday’sLawstatesthatinducedvoltageequalstimerateofchangeoffluxlinkingacoilAmpere’sLawstatesthatprimarycoilMMFisequaltothesecondarycoilMMF7/10/2024Transformers5IdealtransformerandloadFaraday’slaw:v1=e1=N1df/dtv2=e2=N2df/dtv1/v2=N1/N2Ampere’slaw:N1i1=N2i2i1/i2=N2/N1Idealtransformer:v1/v2=N1/N2andi1/i2=N2/N1Losslesssincepowerin=poweroutv1i1=v2i27/10/2024Transformers6IdealtransformerReflectedimpedanceAnimpedanceonthesecondaryofanidealtransformermaybereflectedorreferredtotheprimarybythesquareoftheturnsratio7/10/2024Transformers72.4TransformerreactancesandequivalentcircuitsWeuseacircuitthatisequivalentatitsterminaltoincludethemainnon-idealeffectsofatransformer:LeakagereactancesX1andX2torepresenteffectsofleakagefluxWindingresistancesR1andR2torepresentconductorlossMagnetizingreactanceXmtorepresenteffectsofMMFtomagnetizethecoreCore-lossresistanceRctorepresentcorelosses7/10/2024Transformers87/10/2024Transformers9StepsindevelopmentoftransformerequivalentcircuitPrimaryresistanceandleakagereactance.Magnetizingreactanceandcorelossresistance.Addingidealtransformerandsecondaryimpedance.Reflectingsecondaryimpedancetoprimaryofidealtransformer.ApproximateequivalentcircuitsExcitationbranchimpedancesarelargecomparedtootherbranchesApproximateequivalentcircuitscalledcantilevercircuitsUsetheformthatismostconvenient7/10/2024Transformers10ApproximateequivalentcircuitsAtnormalload,theexcitingcurrentmaybeneglectedForlargepowertransformers,thewindingresistancesaresmall7/10/2024Transformers11Example2.5Example2.5:Atransformersuppliedbyafeeder.NeglectexcitingcurrentReferallparameterstothehigh-voltagesideofthetransformer7/10/2024Transformers12AutotransformersAutotransformersareveryefficientforsmallturnsratios(fromabout1:2to2:1)Efficiencyisgainedbymetallicandmagneticcouplingbetweenprimaryandsecondary7/10/2024Transformers13Three-phasetransformersThreesingle-phasetransformerscanbeconnectedasathree-phasetransformerbankinfourwaysshowninFig.2.19(nextslide)windingsattheleftaretheprimariesthoseattherightarethesecondariesprimarywindinginonetransformercorrespondstothesecondarywindingdrawnparalleltoitSeeExamples2.8and2.9fortypicalcalculations7/10/2024Transformers14Three-phasetransformerconnections7/10/2024Transformers15InstrumenttransformersInstrumenttransformersincludevoltagetransformersandcurrenttransformersVoltagetransformersorpotentialtransformers(PT’s)areusedasalternatingvoltagetransducers,usuallysteppingdownhighvoltagetolowfeedingahighimpedance(e.g.,avoltmeter)Currenttransformers(CT’s)areusedasalternatingcurrenttransducers,usuallysteppingdownhighcurrenttolowfeedingalowimpedance(e.g.,anammeter)7/10/2024Transformers16Per-unitsystemQuantitiessuchasvoltageV,currentI,powerP,reactivepowerQ,apparentpowerS,andimpedanceZ,

canbeexpressedinper-unitformasfollows:7/10/2024Transformers17BaseapparentpowerSisusedasbaseforPandQ:VAbase=Vbase×Ibase

Baseimpedance:Zbase=Vbase/Ibase

Rulesforusingper-unitsystemSelectacommonVAbaseforthesystemSelectabasevoltageatapointinthesystemChooseallotherbasevoltagesinthesameratioastheturnsratioofanytransformerencounteredConvertallquantitiestoperunitonthechosenbasesAnalyzethecircuitinperunitConvertallquantitiestovolts,amperes,etc.bymultiplyingtheirper-unitvaluesbytheircorrespondingbasevalues7/10/2024Transformers18RemarksThisprocedurewillnormallyremovetheidealtransformersintheper-unitcircuitInmostsingletransformerproblems,thebaseVAandvoltagesarechosentobetheratedvalues,whichwillsatisfytherulesonthepreviousslidePowertransformerimpedancesareusuallygiveninpercent,whichis100%timestheper-unitvalueStudyExamples2.12and2.13forillustrationoftheuseofper-unitequations7/10/2024Transformers19SummaryThetransformerisacomponentofacsyste